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1、实验四离散系统分析一、实验目的深刻理解离散时间系统的系统函数在分析离散系统的时域特性、频域特性以及稳定性中的重要作用及意义，熟练掌握利用MATLA分析离散系统的时域响应、 频响特性和零极点的方法。掌握利用 DTFT和DFT确定系统特性的原理和方法。二、实验原理可以在时域、复频域（Z域）及频域分析系统，在以上三种域表征系统固有特性 的量分别为：单位冲激响应h（n）（时域表征）；系统函数H（z） （ Z域表征）；频率响应H（ej ）（频域表征）。MATLA吐要从以上三方面提供了许多可用于分析线性时不变系统的函数，包含 系统时域响应、系统函数、系统频域响应等分析函数。本实验通过调用各种系统预置函数来
2、求系统的以上几个表征量以及零极点图。三、实验内容1.已知某LTI系统的差分方程为：yk 1.143yk 10.412yk20.0675xk0.1349xk 10.0675xk2(1)初始状态y 1 1, y 2 2，输入xk uk，计算系统的全响应。程序段：N=40;b=0.0675,0.1349,0.0675;a=1,-1.143,0.412;x=on es(1,N);zi=filtic(b,a,1,2);y=filter(b,a,x,zi);stem(y)xlabel(k);title(yk);结果:川】7xdkcos(- k)uk;x2【kcos k)uk; X3【k cos(-k)uk
3、10510程序N=30;k=O:N;b=0.0675,0.1394,0.0675;a=1,-1.143,0.412;x1=cos(pi*0.1.*k);x2=cos(pi*0.2*k);x3=cos(pi*0.7*k);y1=filter(b,a,x1);y2=filter(b,a,x2);y3=filter(b,a,x3);subplot(3,1,1);stem(y1)subplot(3,1,2);stem(y2)subplot(3,1,3); stem(y3): 结果：(3)该系统具有什么特性? 答：因果稳定。2.已知某因果LTI系统的系统函数为:H(z)12340.035710.1428
4、z 10.2143z 20.1428z 30.03571z 41 1.035z 10.8264Z 20.2605z 30.04033z 4(1)计算系统的单位冲激响应 程序：N=50;k=1:N;b=0.0357,0.1428,0.2143,0.1428,0.0357; a=1,-1.035,0.8264,-0.2605,0.04033;y1=impz(b,a,N);stem(yl)结果为：(2)当信号通过系统时,c计算4系统的零状态2响应。 程序为：N=50;k=1:N;b=0.0357,0.1428,0.2143,0.1428,0.0357; a=1,-1.035,0.8264,-0.26
5、05,0.04033;x=o nes(1,N)+cos(pi*0.25*k)+cos(0.5*pi*k); y1=impz(b,a,N);y2=filter(b,a,x);subplot(2,1,1);stem(y1)subplot(2,1,2);stem(y2)结果为：CF0.2 -V ：。百 r U 07乞七今七导 OiJO do O牛? 导:卜y M t.- o cinJO 4f so3. 已知LTI系统的输入输出序列分别为xk uk cosqk)uk cos(? k)uk(a) xk (1)kuk, yk 1(1)kuk (!)ku k24 24(b) xk (1)kuk, yk (4
6、)kuk (4)k1uk 1(1)利用解析方法分别求解系统的单位取样响应。程序：N=20;a仁1,-0.75;b仁1.25,-19/16;h1=impz(b1,a1,N);subplot(2,1,1);stem(h1)b2=1,-1;a2=1;h2=impz(b2,a2,N);subplot(2,1,2);stem(h2)结果为：(2)利用系统辨识原理确定并求出系统的单位脉冲响应hk。比较解析方法与系统辨识方法得到的系统单位冲激响应，分析误差原因。程序：N=50;k=O:N;x1=0.5.Ak;y1=0.25*0.5.Ak+0.25.Ak;X1=fft(x1);丫仁fft(y1);H仁 Y1/
7、X1;h1=ifft(H1)n=1:50; n;y2=0.25.A n-4*0.254 n;X2=fft(x2);Y2=fft(y2);H2=Y2/X2;h2=ifft(H2)结果：hi 二H(ej )1. 10F1 十 O.OOOOi h2 二-3.0000 - O.OOOOil误差原因：取样点数不够多引起的误差，而且不易与 k对应4. 已知某离散系统的输入输出序列。输入序列：2, 0.8333，0.3611 ,0.162，0.0748，0.0354，0.017，0.0083，0.0041， 0.002，0.001，0.0005，0.0002，0.0001，0.0001，后面的数值均趋于 0
8、;输出序列：0.0056，-0.0259，0.073，-0.1593，0.297，-0.4974 ,0.7711 ,-1.1267 ,1.5702 ,-2.1037 ,2.724 ,-3.4207 ,4.174 ,-4.9528， 5.7117, -6.3889 , 6.9034 ,-7.1528 , 7.012 ,-6.3322 , 4.9416 ,-2.648 , -0.7564 , 5.4872 , -11.7557 , 19.7533 , -29.6298 , 41.4666 , -55.2433 , 70.7979, -87.7810(1)绘出输入输出信号的波形。程序：x=2,0.8
9、333,0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002, 0.001,0.0005,0.0002,0.0001,0.0001,zeros(1,16);y=0.0056,-0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,1.5702, -2.1037,2.724,-3.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533, -
10、29.6298,41.4666,-55.2433,70.7979,-87.7810; subplot(2,1,1);stem(x)subplot(2,1,2); stem(y) 结果：100501DDo10丄1S-L2510(2)计算该系统的频率响应，并绘出其幅频特性。 程序：x=2,0.8333,0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002, 0.001,0.0005,0.0002,0.0001,0.0001,zeros(1,16);y=0.0056,-0.0259,0.073,-0.1593,0.297,-0.4974,0.771
11、1,-1.1267,1.5702, -2.1037,2.724,-3.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-29.6298,41.4666,-55.2433,70.7979,-87.7810;X=fft(x,128);Y=fft(y,128);H=Y./X;H0=abs(H);plot(H0)结果为：3）计算该系统的单位冲激响应，并绘出其波形程序：x=2,0.8333,0.3611,0.162,0.0748,0.0
12、354,0.017,0.0083,0.0041,0.002, 0.001,0.0005,0.0002,0.0001,0.0001,zeros(1,16);y=0.0056,-0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,1.5702, -2.1037,2.724,-3.4207,4.174,-4.9528,5.7117,-6.3889,6.9034, -7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533, -29.6298,41.4666,-55.2433,7
13、0.7979,-87.7810;X=fft(x,64);Y=fft(y,64);H=Y./X;H0=abs(H);h0=ifft(H0)stem(h0)结果为：hO =Colujims 1 through 566.52S1-35.561420.0669 -12.27466.7&I6CoIujips 昌 through 10-3. 29760, 8766Q.691S-1.6B712.2493CqIujiuis 11through15-2. 50372*552945372. 23S-2.0228CoIujuis 16throneh201. 7587-1, 4926k 2395-1.0850-B04
14、8Coltunns 21through25-0. 63060,4E63-0. 37030.230-0.2136Colmns ZB through 300*3604-0.13530. H5o-0. 1071CL 1033Colrnns 31through35-fl.1027C.1030-0. 10340- 1030-0. 1027Columns 36-through400-1033*0.10710. LI56-0. 13530. 1664匚 oliimns 41through45-0-21360.2804-0, 37030. 4863-0. 6306Colwns 46throvieh500. 8048-1.C0B51. 2395-i 19261+ 7537Colunins 1 through &5-2. 02282.2639-2. 4637Z.5529K5087CdIujiltls 5
